Yes the gas exchange at the surface should be plenty. If you see the surface is stagnant, just adjust/add a powerhead to move the surface a bit. The skimmer does a lot of the oxygenation.
Speaking of skimmers, I agree that the best skimmers are in-sump or stand alone models. Of the three you suggested there's not really one that stands out.
That being said, NO3 at 10 ppm for a FOWLR is more than acceptable. Unless you're having algae problems I wouldn't worry too much about it. With proper husbandry it should go down on it's own.
And yes, it would greatly benefit you to add a sump/fuge. It doesn't take much, and you can add an overflow box so you don;t have to drill your tank. A plastic bin or old 20 gallon tank doesn't take up a lot of room and will make a big difference.
Water changes not only remove waste but possibly re-introduce elements that have been used up by the tank inhabitants, so make sure you continue them.